10n/n^2+16=1

Solution for 10n/n^2+16=1 equation:

10n/n^2+16=1

We move all terms to the left:

10n/n^2+16-(1)=0


Domain of the equation: n^2!=0

n^2!=0/

n^2!=√0

n!=0

n∈R


We add all the numbers together, and all the variables

10n/n^2+15=0

We multiply all the terms by the denominator


10n+15*n^2=0

We add all the numbers together, and all the variables

15n^2+10n=0

a = 15; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·15·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*15}=\frac{-20}{30}
=-2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*15}=\frac{0}{30}
=0
$